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Related Concept Videos

Strain-Energy Density01:20

Strain-Energy Density

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Understanding the strain energy density in materials under axial load is crucial for evaluating their mechanical behavior and durability. When a rod is subjected to such a load, it elongates and stores energy, known as strain energy, as potential energy within the material. This energy is measured in terms of energy per unit volume.
In the elastic region of a material, the relationship between the stress and the strain is linear and follows Hooke's Law. The strain energy density in this region...
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To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...
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The universe is composed of matter in different forms, and all forms of matter contain energy.  The different forms of energy on Earth originate from the Sun — the ultimate energy source. Plants capture light energy from the Sun, and, via the process of photosynthesis, convert it into chemical energy. This stored energy from plants can be harnessed in many ways. For example, eating plant products as food provides energy for our body to function, and burning wood or coal (fossilized...
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Free Energy01:21

Free Energy

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Free energy—abbreviated as G for the scientist Gibbs who discovered it—is a measurement of useful energy that can be extracted from a reaction to do work. It is the energy in a chemical reaction that is available after entropy is accounted for. Reactions that take in energy are considered endergonic and reactions that release energy are exergonic. Plants carry out endergonic reactions by taking in sunlight and carbon dioxide to produce glucose and oxygen. Animals, in turn, break...
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Energy Basics02:27

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Chemical reactions, such as those that occur when you light a match, involve changes in energy as well as matter.
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Internal Energy02:00

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The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Suppose a system with initial internal energy, Uinitial, undergoes a change in energy (transfer of work or heat), and the final internal energy of the system is Ufinal. Change in internal energy equals the difference between Ufinal and Uinitial.
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Related Experiment Video

Updated: Jan 22, 2026

Energy Dispersive X-ray Tomography for 3D Elemental Mapping of Individual Nanoparticles
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Dispersion Energy from Local Polarizability Density.

Muhammad Shahbaz1, Krzysztof Szalewicz1

  • 1Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA.

Physical Review Letters
|July 9, 2019
PubMed
Summary

A new, simple nonlocal functional improves dispersion energy calculations. This method uses regularization and dynamic polarizability density for significantly more accurate results in molecular dimers.

Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Theoretical physics

Background:

  • Accurate calculation of dispersion energies is crucial for understanding molecular interactions.
  • Existing nonlocal functionals often face challenges with singularities and accuracy.

Purpose of the Study:

  • To propose a novel, simple nonlocal functional for calculating dispersion energies.
  • To enhance accuracy and overcome limitations of previous methods.

Main Methods:

  • Introduction of a regularization technique to eliminate singularities.
  • Incorporation of dynamic polarizability density, inspired by van der Waals density functionals.
  • Testing the functional's performance on dispersion energies of representative molecular dimers.

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Main Results:

  • The proposed nonlocal functional demonstrates significantly improved accuracy.
  • The regularization and dynamic polarizability density contribute to enhanced performance.
  • The new functional outperforms previously published nonlocal functionals for dispersion energy calculations.

Conclusions:

  • The developed simple nonlocal functional offers a more accurate approach to dispersion energy calculations.
  • This method provides a valuable tool for theoretical chemistry and materials science.
  • Further applications in predicting molecular properties are promising.